Quantum Optical Simulator for Unruh-DeWitt Detector Dynamics

Abstract

We present a quantum-optical platform for simulating relativistic detector-field interactions using entangled nonlinear biphoton sources (ENBSs), realized through phase-controlled single-photon frequency-comb (SPFC) sources. By mapping the dynamical evolution of this system onto the Unruh-DeWitt (UDW) detector model, we show that signal-mode excitations emulate detector transitions driven by vacuum fluctuations, while coherently seeded idler modes act as an effective quantum field. This correspondence enables tabletop exploration of Unruh-like excitation, coherence harvesting, and field-induced entanglement. We derive the effective interaction Hamiltonian and Lindblad master equation for two coherently seeded ENBS units and obtain analytical solutions for the signal photon number \(N_{\rm sig}(t)\) and second-order correlation function \(g^{(2)}(0;t)\). Numerical simulations confirm that phase-dependent biphoton dynamics reproduce UDW-type behavior, including tunable excitation and quantum correlations. The output signal state exhibits controllable fidelity, interference visibility, and entanglement entropy as functions of the seeding phase and amplitude. These results establish ENBSs as experimentally accessible quantum simulators of relativistic field phenomena, providing a photonic testbed for analog gravitational effects, vacuum fluctuations, and spacetime-induced coherence-all within reach of current nonlinear-optics technology.

Figures (5)

• Figure 1: Quantum-optical analog simulator of Unruh–DeWitt detector dynamics. Two entangled nonlinear biphoton sources (ENBSs), each realized using a seeded single-photon frequency-comb (SPFC) generator, are implemented with periodically poled lithium niobate (PPLN) crystals pumped by optical frequency combs. Coherent seed fields at 1542 nm with a controllable relative phase $\Delta\phi_{\text{sd}}$ are injected into the idler paths. The resulting signal outputs at 807 nm exhibit quantum correlations analogous to Unruh–DeWitt detector excitations mediated by a shared vacuum field. The mean photon number $N_{\rm sig}(t)$ is measured by removing the beam splitter (BS), while the second-order correlation function $g^{(2)}(0;t)$ is obtained via coincidence detection at the two outputs. Alternatively, when a single detector is placed after the combining BS, the setup measures the first-order (single-photon) coherence of the signal field—demonstrating phase-sensitive interference as in Refs. Lee2018Yoon2021. BS: beam splitter; VBS: variable beam splitter; SPSD: single-photon-sensitive detector.
• Figure 2: Signal photon number dynamics with and without damping. The mean photon number $N_{\text{sig}}(t)$ is shown for $|\alpha| = 5$ and $|g_{\rm eff}| = 1~\text{GHz}$, comparing the undamped case (solid line) with the damped case (dashed line) for $\kappa_s / (2\pi) = 3~\text{GHz}$. Saturation occurs within the 75 ps group delay corresponding to a 1-cm PPLN crystal at 807 nm. This illustrates how signal growth is limited by decoherence, analogous to finite-time switching in relativistic detector models. For the asymmetric driving case, see Fig. S1 in the SI.
• Figure 3: Contour plot of $g^{(2)}(0; t=75~\mathrm{ps})$ as a function of the local phase $\Phi_N = |\Delta\phi_p - \Delta\phi_{sd}|$ and global phase $\Phi = |\Delta\phi_p - (\Delta\phi_s + \Delta\phi_{sd})|$, for $|\alpha| = 2$ and $|g_{\mathrm{eff}}| / (2\pi) = 1~\mathrm{GHz}$. Maximal bunching occurs near $(\Phi_N, \Phi) = (\pi, \pi/2)$, revealing the nonlinear interplay between destructive local amplification and enhanced nonlocal quantum correlations.
• Figure 4: Fidelity $F(\Delta\phi_{\text{sd}})$, defined as the conditional quantum overlap between the idler states $|\alpha_1,1\rangle|\alpha_2\rangle$ and $|\alpha_1\rangle|\alpha_2,1\rangle$, plotted as a function of the relative seeding phase $\Delta\phi_{\text{sd}}$ for symmetric amplitudes $|\alpha| = 1,~4,~10$. The fidelity reaches a maximum at $\Delta\phi_{\text{sd}} = 0$ and $2\pi$, and exhibits a minimum at $\pi$, where the signal outputs become most entangled due to reduced path indistinguishability. As $|\alpha|$ increases, $F \to 1$ uniformly, reflecting the classical-like coherence of strongly seeded idler states. See Fig. \ref{['Fig5']} for corresponding visibility and entanglement, and Figs. S2 and S5 for asymmetric cases in the SI.
• Figure 5: Plots of fidelity $F(\Delta\phi_{\text{sd}})$ (red), visibility $\mathcal{V}(\Delta\phi_{\text{sd}})$ (blue), and entanglement $\mathcal{E}(\Delta\phi_{\text{sd}})$ (magenta) for symmetric seeding amplitudes $|\alpha_1| = |\alpha_2| = 2$, yielding equal signal-mode populations $\rho_{11} = \rho_{22} = 0.5$. The fidelity and visibility reach their minimum at $\Delta\phi_{\rm sd} = \pi$, where the signal outputs become maximally distinguishable and entanglement is maximized. As $\Delta\phi_{\rm sd} \to 0$ or $2\pi$, $F \to 1$ and $\mathcal{E} \to 0$, indicating high coherence and low entanglement. For asymmetric seeding cases, see Figs. S2--S5 in the SI.